Implement subset sum using backtracking (rust-lang#765)

* feat[backtracking]: implement subset sum

* chore(docs): add docstring

* chore: format code

* chore: change `i32` to `isize`

* docs: remove redundant comment

Author: sozelfist

src/backtracking/mod.rs

@@ -6,6 +6,7 @@ mod n_queens;
 mod parentheses_generator;
 mod permutations;
 mod rat_in_maze;
+mod subset_sum;
 mod sudoku;
 
 pub use all_combination_of_size_k::generate_all_combinations;
@@ -16,4 +17,5 @@ pub use n_queens::n_queens_solver;
 pub use parentheses_generator::generate_parentheses;
 pub use permutations::permute;
 pub use rat_in_maze::find_path_in_maze;
+pub use subset_sum::has_subset_with_sum;
 pub use sudoku::sudoku_solver;

src/backtracking/subset_sum.rs

@@ -0,0 +1,55 @@
+//! This module provides functionality to check if there exists a subset of a given set of integers
+//! that sums to a target value. The implementation uses a recursive backtracking approach.
+
+/// Checks if there exists a subset of the given set that sums to the target value.
+pub fn has_subset_with_sum(set: &[isize], target: isize) -> bool {
+    backtrack(set, set.len(), target)
+}
+
+fn backtrack(set: &[isize], remaining_items: usize, target: isize) -> bool {
+    // Found a subset with the required sum
+    if target == 0 {
+        return true;
+    }
+    // No more elements to process
+    if remaining_items == 0 {
+        return false;
+    }
+    // Check if we can find a subset including or excluding the last element
+    backtrack(set, remaining_items - 1, target)
+        || backtrack(set, remaining_items - 1, target - set[remaining_items - 1])
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    macro_rules! has_subset_with_sum_tests {
+        ($($name:ident: $test_case:expr,)*) => {
+            $(
+                #[test]
+                fn $name() {
+                    let (set, target, expected) = $test_case;
+                    assert_eq!(has_subset_with_sum(set, target), expected);
+                }
+            )*
+        }
+    }
+
+    has_subset_with_sum_tests! {
+        test_small_set_with_sum: (&[3, 34, 4, 12, 5, 2], 9, true),
+        test_small_set_without_sum: (&[3, 34, 4, 12, 5, 2], 30, false),
+        test_consecutive_set_with_sum: (&[1, 2, 3, 4, 5, 6], 10, true),
+        test_consecutive_set_without_sum: (&[1, 2, 3, 4, 5, 6], 22, false),
+        test_large_set_with_sum: (&[5, 10, 12, 13, 15, 18, -1, 10, 50, -2, 3, 4], 30, true),
+        test_empty_set: (&[], 0, true),
+        test_empty_set_with_nonzero_sum: (&[], 10, false),
+        test_single_element_equal_to_sum: (&[10], 10, true),
+        test_single_element_not_equal_to_sum: (&[5], 10, false),
+        test_negative_set_with_sum: (&[-7, -3, -2, 5, 8], 0, true),
+        test_negative_sum: (&[1, 2, 3, 4, 5], -1, false),
+        test_negative_sum_with_negatives: (&[-7, -3, -2, 5, 8], -4, true),
+        test_negative_sum_with_negatives_no_solution: (&[-7, -3, -2, 5, 8], -14, false),
+        test_even_inputs_odd_target: (&[2, 4, 6, 2, 8, -2, 10, 12, -24, 8, 12, 18], 3, false),
+    }
+}